The main difference between [1]} and this work is again in the density structure, which is affected by the need to use a non-zero gravitational smoothing length (\(\sim \)  fraction of \({R_{\textnormal {Hill}}}\) ) and large grid cells (\(\sim R_{\mathrm {J}}\) ), due to the fact that these are three-dimensional, global-disc and thus numerically expensive simulations. Judging by the density structures seen in their Figure 4, there is likely also a considerable amount of variability. Consequently, estimating
the mean influx rate would require dozens of snapshots.
Therefore, the extinction might be calculated more accurately in our work but our density structure is simplified and thus approximate, albeit in a different way.
The reader is refered to Appendix B of [2]} and also [3]}
for the more important discussion of how the emission was computed in [1]}.
